The issue is feedback. Something feeding voltage to the coil. Your test is valuable. But most folks are following the "instruction" to run the wire to ignition "ON".
So without knowing what actual switch you have, what harness you have and if you wired it per instructions or wired to the ACC fuse yourself, the bottom line is that it's impossible to say if you have a feedback path when switch is off, at this point. I think I said each case is different and some who have a direct wire, no bulb, have run-on and some don't.
There are at least two "original" solenoid switches available. The ACC function is different for each.
You may have proven something and may not. You did prove you don't need a bulb. Glad you are keeping it for a warning.
I thought you added a bypass wire, sorry, I see you just put in a piece of metal into the wedge base style socket.
